Question

what is the approximate value of x? round to the nearest tenth. triangle with right angle at top, left leg labeled x, right leg labeled y, bottom side labeled 6 cm, bottom - right angle labeled 50° options: 3.1 cm, 3.9 cm, 4.6 cm, 5.4 cm

Explanation:

Step1: Identify triangle type and trigonometric relation

The triangle is right - angled. For the angle of \(50^{\circ}\), the side \(x\) is opposite to the angle, and the hypotenuse is \(6\) cm. We use the sine function, where \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(50^{\circ})=\frac{x}{6}\).

Step2: Solve for \(x\)

We can re - arrange the formula to \(x = 6\times\sin(50^{\circ})\). We know that \(\sin(50^{\circ})\approx0.7660\). Then \(x=6\times0.7660 = 4.596\approx4.6\) (rounded to the nearest tenth).

Answer:

4.6 cm